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Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation
P. C. B. Phillips
Abstract
Edgeworth series expansions are obtained of the finite sample distributions of the least squares estimator and the associated t ratio test statistic in the context of a first-order noncircular stochastic difference equation. General formulae are given for these expansions up to 0(T^-1) where T is the sample size and explicit representations of these in terms of the true parameters are derived up to 0(T^-1/2). Some numerical comparisons of the approximations and the exact distributions are made in the case of the least squares estimator.
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